Construction of a net without transversals over a non-planar near-field
Construction of codes identifying sets of vertices.
Construction of extended Steiner systems for information retrieval.
Construction of finite -groups with prescribed group of noncentral automorphisms
Construction of Mendelsohn designs by using quasigroups of -varieties
Let be a positive integer. An algebra is said to have the property if all of its subalgebras generated by two distinct elements have exactly elements. A variety of algebras is a variety with the property if every member of has the property . Such varieties exist only in the case of prime power. By taking the universes of the subalgebras of any finite algebra of a variety with the property , , blocks of Steiner system of type are obtained. The stated correspondence between Steiner...
Construction of Menon designs with parameters (784,378,182) and (900,435,210).
Construction of minimal bracketing covers for rectangles.
Construction of Perpendicular Steiner. Quasigroups
Construction of Perpendicular Steiner Quasigroups. (Short Communications).
Construction of quasigroups having a large number of orthogonal mates
Construction of Skew Room Squares.
Construction of solvable near-block designs with the aid of a computer. (Konstruktion auflösbarer Fast-Blockpläne mit Hilfe eines Computers.)
Construction of the mutually orthogonal extraordinary supersquares
Our purpose is to determine the complete set of mutually orthogonal squares of order d, which are not necessary Latin. In this article, we introduce the concept of supersquare of order d, which is defined with the help of its generating subgroup in . We present a method of construction of the mutually orthogonal supersquares. Further, we investigate the orthogonality of extraordinary supersquares, a special family of squares, whose generating subgroups are extraordinary. The extraordinary subgroups...
Construction, properties and applications of finite neofields
We give a short account of the construction and properties of left neofields. Most useful in practice seem to be neofields based on the cyclic group and particularly those having an additional divisibility property, called D-neofields. We shall give examples of applications to the construction of orthogonal latin squares, to the design of tournaments balanced for residual effects and to cryptography.
Constructions for cubic graphs with large girth.
Constructions for resolvable and related designs.
Constructions for type I trees with nonisomorphic Perron branches
A tree is classified as being type I provided that there are two or more Perron branches at its characteristic vertex. The question arises as to how one might construct such a tree in which the Perron branches at the characteristic vertex are not isomorphic. Motivated by an example of Grone and Merris, we produce a large class of such trees, and show how to construct others from them. We also investigate some of the properties of a subclass of these trees. Throughout, we exploit connections between...
Constructions of color schemes
Constructions of representations of rank two semisimple Lie algebras with distributive lattices.
Constructions over tournaments
We investigate tournaments that are projective in the variety that they generate, and free algebras over partial tournaments in that variety. We prove that the variety determined by three-variable equations of tournaments is not locally finite. We also construct infinitely many finite, pairwise incomparable simple tournaments.